3d chess pieces from bezier curves
Check this on changing the origin of the imported SVG curves: Change pivot or local origin of an object

I imported the SVG from Illustrator, changed the origin point and added a screw modifier. One thing to note, my imported SVG curve was a closed shape. I deleted a curve segment on the axis I wanted to spin around by selecting the two curve point that made the segment, right-clicked and chose "delete segment".

Here's a file you can see an example.